A comparison between T-S fuzzy systems and affine T-S fuzzy systems as nonlinear control system models

In model based fuzzy control, almost all considered control system models are T-S and affine T-S fuzzy control systems. However, there is a lack of systematic and theoretic understanding what the similarity and difference between these two dominated fuzzy control systems models to provide the guidance to choose the right models to the right application problems. To fill in such a gap, this paper gives a systematic comparison between T-S and affine T-S fuzzy control systems. The main results obtained are, firstly, the similarity between T-S and affine T-S fuzzy control systems is that both can and can only approximate affine nonlinear control models and have the similar representation capability for smooth (continuous differentiable) nonlinear control systems. As a result, T-S fuzzy systems are better choice as the stabilization analysis and control design simpler; Secondly, one of the main dissimilarities is that affine T-S fuzzy systems have better representation for continuous only (i.e., not differentiable) nonlinear control systems and can accurately approximate some continuous only nonlinear systems which cannot be accurately represented by T-S fuzzy systems. Another main dissimilarity is that affine T-S fuzzy systems are more accurate when representing high dimensional nonlinear systems. As a result, affine T-S fuzzy systems often could be the better choice for non-smooth or high dimensional nonlinear control systems.